By amplifying the cascaded random Raman fiber laser (RRFL) oscillator and ytterbium fiber laser oscillator, we present the first, to the best of our knowledge, demonstration of a 10-kW-level high-spectral-purity all-fiber ytterbium-Raman fiber amplifier (Yb-RFA). With a carefully designed backward-pumped RRFL oscillator structure, the parasitic oscillation between the cascaded seeds is avoided. Leveraging the RRFL with full-open-cavity as the Raman seed, the Yb-RFA realizes 10.7-kW Raman lasing at 1125 nm, which is beyond the operating wavelengths of all the reflection components used in the system. The spectral purity of the Raman lasing reaches 94.7% and the 3-dB bandwidth is 3.9 nm. This work paves a way to combine the temporal stability of the RRFL seed and the power scaling of Yb-RFA, enabling the wavelength extension of high-power fiber lasers with high spectral purity.